John Nash crumples paper

Some of you might have seen the movie called “A Beautiful Mind” showered by Academy Awards starring Russell Crowe. It depicts the epic journey of a genius mathematician who went crazy and then got a Nobel Prize in Economics.

Hollywood loves these kinds of stories.

Watch the movie.

The real Nash did not get an Oscar but he got a Nobel for his contributions in “game theory” applied to finance.

(Everyone knows the possibly apocryphal story that Nobel did not have a prize for math because his wife had multiple affairs with some hunky math dude like the one depicted by Russell Crowe)

Mathematicians on the other hand celebrate Nash’s work for a completely different reason. Math dudes love his work on isometric embedding. Let me sort of explain what is going on with an analogy of some sorts.

Take a piece of paper and crumple it. It is still a piece of paper and if you draw a line on the initial piece of paper it will draw a jagged line on the crumpled one. However these two lines will have the same length. That is roughly what isometric means. In other words you transform a shape into another shape while preserving distances. In Greek: iso (same) metric (length).

Duh obvious and what is the big deal?

Try to crumple a piece of paper while preserving distances and at the same time forcing it to stay on your coffee table top.

Hah not so easy!

Try this at home.

To preserve distances you have to wander off your table into three-dimensional space. That is where the paper sheet can freely crumple and preserve distances. You have to have at least one additional dimension to crumple that paper sheet properly. Higher dimensions are a bonus. Nash proved that this is true not only for a paper sheet but for any shape of any dimension. This problem is obvious to state but hard to prove.

Here is Nash’s recommendation letter from his professor when he applied to Princeton.

Sweet and short and to the point and he was accepted at Princeton where he did some of his groundbreaking work.

Cars and Mathematicians do not mix well, even if they do not drive.

“Mathematician John Nash, the Nobel winner who inspired the film A Beautiful Mind, has been killed in a car accident along with his wife in New Jersey. He was 86. Nash and his wife, Alicia Nash, 82, were in a taxi accident Saturday, New Jersey State Police Sergeant First Class Gregory Williams told CBC News.”

On a happier note, check out this awesome explanation of one of his famous theorems.